Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

Abstract

An enhanced method able to perform accurate stability of constrained uncertain systems is presented. The main objective of this method is to compute a sequence of feedback control laws which stabilizes the closed-loop system. The proposed approach is based on robust model predictive control (RMPC) and enhanced maximized sets algorithm (EMSA), which are applied to improve the performance of the closed-loop system and achieve less conservative results. In fact, the proposed approach is split into two parts. The first is a method of enhanced maximized ellipsoidal invariant sets (EMES) based on a semidefinite programming problem. The second is an enhanced maximized polyhedral set (EMPS) which consists of appending new vertices to their convex hull to minimize the distance between each new vertex and the polyhedral set vertices to ensure state constraints. Simulation results on two examples, an uncertain nonisothermal CSTR and an angular positioning system, demonstrate the effectiveness of the proposed methodology when compared to other works related to a similar subject. According to the performance evaluation, we recorded higher feedback gain provided by smallest maximized invariant sets compared to recently studied methods, which shows the best region of stability. Therefore, the proposed algorithm can achieve less conservative results.

Enlarging the region of stability in robust model predictive controller based on dual-mode control

“…Wan and Kothare (2003b) have proposed another efficient RMPC algorithm with a time varying terminal constraint set that not only enlarges the stability region but also reduces on-line computation. Hamdi et al (2020) introduced a combination of RMPC method and maximized invariant sets procedure based on a semidefinite programming problem that could enhance the stability region. An off-line RMPC algorithm based on polyhedral invariant set (instead of ellipsoidal invariant set) was developed by Bumroongsri and Kheawhom (2012) that yields a substantial expansion of the stabilizable region.…”